Structural and transport properties of double perovskite Dy2NiMnO6

Materials Research Bulletin 62 (2015) 153–160

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Structural and transport properties of double perovskite Dy2NiMnO6 Sadhan Chanda *, Sujoy Saha, Alo Dutta, T.P. Sinha Department of Physics, Bose Institute, 93/1, Acharya Prafulla Chandra Road, Kolkata 700009, India

A R T I C L E I N F O

A B S T R A C T

Article history: Received 10 June 2014 Accepted 8 November 2014 Available online 11 November 2014

The double perovskite oxide Dy2NiMnO6 (DNMO) is synthesized in nano and bulk phase by the sol–gel citrate method. The Rietveld refinement of X-ray diffraction pattern of the sample at room temperature shows the monoclinic P21/n phase. Dielectric relaxation of the sample is investigated in the impedance and electric modulus formalisms in the frequency range from 50 Hz to 1 MHz and in the temperature range from 253 to 415 K. The Cole–Cole model is used to explain the relaxation mechanism in DNMO. The frequency-dependent maxima in the imaginary part of impedance are found to obey an Arrhenius law with activation energy of 0.346 and 0.344 eV for nano and bulk DNMO, respectively. A significant increase in conductivity of bulk DNMO has been observed than that of the nanoceramic. Electronic structures and magnetic properties of DNMO have been studied by performing first principles calculation based on density functional theory. ã 2014 Elsevier Ltd. All rights reserved.

Keywords: A. Ceramics B. Sol–gel chemistry C. Impedance spectroscopy D. Dielectric properties E. Electronic structure

1. Introduction Multifunctional double perovskite oxides (DPOs) Ln2NiMnO6 [Ln = lanthanides] have gained immense research interest in the recent years due to their rich physical properties which make them as the prospective materials for technological applications [1–13]. In this family La2NiMnO6 having ferromagnetic order temperature of about 280 K is a rare example of a single material platform with multiple functions, inwhich the spins, electric charges, and dielectric properties can be tuned by magnetic and/or electric fields. The dielectric relaxor behaviour is also observed in Nd2NiMnO6 by Shi et. al [4]. These properties make this series of materials suitable for possible applications in spintronic devices, such as magnetic memories and magnetodielectric capacitors [2,6]. Most of the reported Ln2NiMnO6 DPOs have been prepared by high temperature solid-state reaction technique from their corresponding pure oxides. But in many cases this technique suffers from the problem of the presence of some unreacted rare earth oxides as impurities in the materials and sometimes the formation of undesirable phases [7]. It is observed that probability of getting the impurity phases increases when the ionic radius of the rare earth element in this series decreases [11,12]. In this respect while synthesising Tb2NiMnO6 by solid state reaction technique, the existence of an impurity phase of Tb2O3 is reported by Nair et al. [11]. Similarly, Y2NiMnO6 [12] has not been synthesised in single phase

* Corresponding author. Tel.: +91 33 23031191/9836626460; fax: +91 33 23506790. E-mail addresses: [email protected], [email protected] (S. Chanda). http://dx.doi.org/10.1016/j.materresbull.2014.11.021 0025-5408/ ã 2014 Elsevier Ltd. All rights reserved.

because radius of Y3+ is almost equal to Dy3+. Thus, synthesizing a pure phase material of this family with lower ionic radius (such as Y, Dy–Lu compounds) is challenging. Among the various Ln2NiMnO6 DPOs studied so far, Dy2NiMnO6 (DNMO) is a ferromagnetic material with Tc
105 K. Asai et al. have studied the crystal structure and magnetic properties of DNMO and concluded that superexchange interaction Ni2+–O–Mn4+ is responsible for ferromagnetism in this material [7]. The theoretical effort for understanding the various microscopic properties of DNMO is not available in the literature. To our knowledge, there exists no report of plane wave based basic electronic structure calculation of DNMO. In the present work, we have successfully synthesised a pure phase of DNMO by sol–gel citrate method. The dielectric properties of the sample have been investigated by alternating current impedance spectroscopy (ACIS) in a frequency range from 50 Hz to 1 MHz and in the temperature range from 253 K to 415 K. The study of the influence of sintering conditions (effects of grain size) on the electrical properties of the ceramic has also been reported. We have carried out the spin polarised density functional theory calculations using full potential linearized augmented plane wave (FPLAPW) method implemented in WIEN2k [14] to understand the ferromagnetic insulating behaviour in this compound. 2. Experimental 2.1. Sample preparation DNMO in powder form was synthesized by the sol–gel citrate method [15,16]. At first, reagent grade Dy(NO3)36H2O (Alfa Aesar),

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Ni(NO3)24H2O (Alfa Aesar), and Mn(NO3)26H2O (Alfa Aesar) were taken in stoichiometry ratio and separately dissolved in de-ionized water by stirring with a magnetic stirrer. The obtained clear solutions were then mixed together. Citric acid (CA) and ethylene glycol (EG) were added to this solution drop wise according to the molar ratio of {Dy3+, Ni2+ + Mn2+}:{CA}:{EG} = 1:1:4 to form a polymeric-metal cation network. The solution was stirred at 348 K using a magnetic stirrer for 4 h to get a homogeneous mixture and then the solution was dried at 393 K to obtain the gel precursor. At the end, combustion had taken place in the gel which had produced a black fluffy powder of the material. The powder was calcined at 1073 K in air for 5 h and cooled down to room temperature (RT
300 K) at a cooling rate of 1 K/min. The calcined sample was pelletized into discs of thickness = 1.5 mm and diameter = 8 mm using polyvinyl alcohol as binder. Finally, these pellets were sintered at 1073 and 1423 K for 10 h in air and cooled down to RT by cooling at the rate of 1 K/min. From now onwards, we have abbreviated DNMO-1 and DNMO-2 for the samples sintered at 1073 and 1423 K, respectively.

approximation corresponding to potential is taken into account. In the calculations, we have used a parameter RMTKmax = 7, which determines matrix size (convergence), where Kmax is the plane wave cut-off and RMT is the smallest of all atomic sphere radii. For the self-consistent calculation with the plane wave basis 4  4  4 Monkhorst-Pack [19] k point mesh is used. The iteration process is continued until calculated total energy and charge density of the crystal converged and becomes less than 0.01 mRy/ unit cell and 0.001 e/a.u.3, respectively. For the 3d transition metal (Ni and Mn) and rare earth element (Dy) the correlation effect of localized d and f electrons are considered. We have applied the effective Coulomb potential (UNi  3d = UMn3d = 2 eV and UDy4f = 4 eV) in GGA + U [20] calculations. The value of U is optimized such that the moments of the magnetic ions and optical band gap are satisfactorily described with respect to the experimental results.

2.2. Sample characterization

The X-ray diffraction pattern of DNMO-1 is shown in Fig. 1, where the symbols represent the experimental data and the solid line represents the best fit to the diffraction data obtained by Rietveld refinement for monoclinic symmetry (space group P21/n). The curve at the bottom represents the difference between experimental pattern and the calculated one. The refined lattice parameters, a = 5.2425(4) Å, b = 5.5468(5) Å, c = 7.5025(7) Å, and the monoclinic angle b = 90.042(2) are in reasonable agreement with the same series of materials such as Tb2NiMnO6 [11] and Ln2NiMnO6 (Ln¼Nd, Sm) [9]. The stability of DNMO to a first approximation is determined by the ratio of Dy—O to B—O (B¼Ni, Mn) bond lengths, which can be expressed as the tolerance factor pffiffiffi Tf = ðrDy þ r0 Þ=ð 2ððrNi þ rMn Þ=2 þ r0 ÞÞ (where rDy, rNi, rMn, and ro are ionic radii of dysprosium, nickel, manganese, and oxygen, respectively). Here Dy has co-ordination number eight instead of 12. The reduced coordination number of Dy is a result of some of the anions moving too far away for lower symmetry DPO due to octahedral tilting which causes the first coordination sphere about the Dy cation to change. It has been proposed by Woodward [21] that any anion more than 3.00 Å away from the A-cation of DPOs (general formula A2B0 B00 O6) may be considered to be outside the coordination sphere. It is found that Tf = 0.85 for DNMO using rDy = 1.027 Å, rNi = 0.69 Å, rMn = 0.53 Å, and ro = 1.4 Å [22]. A schematic presentation of the DNMO cell is shown in the inset of Fig. 1 with the distribution of ions at crystallographic positions 4e for

The determination of lattice parameters and the identification of the phase at RT was carried out using a X-ray powder diffractometer (Rigaku Miniflex II) having Cu-Ka radiation in the 2u range of 15–80 by scanning at 0.02 per step. The refinement of crystal structure was performed by the Rietveld method with the Fullprof program [17]. The background was fitted with 6coefficients polynomial function, while the peak shapes were described by pseudo-Voigt profiles. Throughout the refinement, scale factor, lattice parameters, positional coordinates (x, y, z), and thermal parameters were varied and the occupancy parameters of all the ions were kept fixed. The particle size and selected area electron diffraction (SAED) pattern of the sample (DNMO-1) were studied by the high resolution transmission electron microscopy (HRTEM) (FEI Tecnai G2, 200 KV). The scanning electron microscope (FEI Quanta 200) was used for investigation of the homogeneity of the synthesized samples. The optical spectrum of the material was collected by a Shimadzu UV–vis spectrometer. For electrical measurements, both the sides of sintered pellets were polished. Two thin gold plates were used as electrodes. The impedance, conductance, and phase angle were measured using an LCR meter (HIOKI) in the frequency range from 50 Hz to 1 MHz at the oscillation voltage of 1.0 V. The measurements were performed over the temperature range from 253 K to 415 K using an inbuilt cooling–heating system. The temperature was controlled by an Eurotherm 2216e programmable temperature controller connected with the oven. Each measured temperature was kept constant with an accuracy of 1 K. The complex dielectric modulus M* (=jvCoZ*) was obtained from the temperature dependence of the real (Z0 ) and imaginary (Z00 ) components of the complex impedance Z* (=Z0 + iZ00 ), where v is the angular frequency pffiffiffiffiffiffiffi (v = 2 pn) and i = 1. Co = eoA/d is the empty cell capacitance, where A is the sample area, and d is the sample thickness. The I–V characteristics of DNMO were measured in the temperature range from 213 K to 473 K using a source measure unit (Keithley 236).

3. Results and discussion 3.1. Structural analysis

2.3. Computational details The experimental lattice parameters are used as the input for the FPLAPW calculations of DNMO. The muffin-tin (MT) radii for Dy, Ni, Mn, and O are taken as 2.21, 1.96, 1.91, and 1.65 au (atomic unit), respectively. To take into account the exchange and correlation effects, generalized gradient approximation (GGA) as parametrized by Perdew et al. [18] has been applied. No shape

Fig. 1. Rietveld refinement plot of DNMO-1 at room temperature. A schematic presentation of the DNMO monoclinic unit cell is shown in the inset. The Ni atoms are located at the centres of the NiO6 (orange) octahedra. The Mn atoms are located at the centres of the MnO6 (green) octahedral. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Table 2 Lattice constant, grain size, porosity, and activation energy for DNMO-1 and DNMO2 samples. Grain size (mm)

Ea(eV)

15.5

0.178  0.023

0.364

8.5

0.289  0.067

0.344

Samples

Lattice parameters (Å)

Density Porosity (%) (gm/cc)

DNMO-1

a = 5.2425, b = 5.5469 c = 7.5026, b = 90.042 a = 5.2446, b = 5.5477 c = 7.5044, b = 90.045

6.87

7.45

DNMO-2

O2 ions, constituting NiO6 and MnO6 octahedra, respectively. A quantitative estimate of the valence states of the cations was obtained by calculating the bond valence sums (BVS). The final structure parameters along with important bond distances, bond angles associated with NiO6 and MnO6 octahedra and BVS of DNMO are listed in Table 1. The measured lattice parameters, density and porosity of the samples sintered at different temperatures are given in Table 2. The density of the samples increases as the sintering temperature increases from 1073 to 1473 K. On the other hand, porosity (P) of the samples decreases with the increase of sintering temperature. The HRTEM micrographs of DNMO-1 are shown in Fig. 2(a–c). The particles are found to be segregated as observed from Fig. 2(a). The sizes of the particles are estimated to be in the range from 80 to 110 nm. Fig. 2(b) indicates the homogeneous orientation of the lattice planes with interplanar spacing of 0.27 nm which correlates with the d spacing value of (0 2 0) plane of the XRD pattern. The SAED pattern (Fig. 2(c)) shows bright spots indicating that particles are well crystalline in nature. The surface morphology of DNMO samples is revealed by SEM, as shown in Fig. 3(a) and (b). It is clear that the grain size increases with increasing the sintering temperature. The mean grain sizes are about 0.178  0.023 and 0.289  0.067 mm for DNMO-1 and DNMO-2 samples, respectively. It is observed that with the increase in sintering temperature, the number of pores decreased and the rate of grain growth apparently increased. 3.2. Optical analysis

Fig. 2. (a) The transmission electron microscopy (TEM) image of particles, (b) its corresponding high resolution-TEM (HR-TEM) image, and (c) selected area electron diffraction (SAED) pattern.

Dy3+ ions, 2c for Ni2+ ions, 2d for Mn4+ ions and 4e for O2 ions as given in Table 1. Each Ni2+ and Mn4+ ions are surrounded by six

The UV–vis absorption spectrum of DNMO-1 is shown in Fig. 4. The energy band gap is determined using absorption spectrum with the help of Tauc relation [23,24] given by   ahn ¼ A hn  Eg n (1) where hy is the energy of the incident photon, a is the absorption coefficient, and A is a characteristic parameter independent of the photon energy, Eg is the optical band gap and the value of n is 1/2 or

Table 1 Structural parameters for DNMO as obtained from Rietveld analysis of XRD pattern. Space group = p21/n,a = 5.2425(4) Å, b = 5.5468(5) Å, c = 7.5025(7) Å, and b = 90.042(2) Atoms

Site

4e Dy Ni 2c Mn 2d O1 4e O2 4e O3 4e BVS: Dy = 2.8, Ni = 2.57, Mn = 3.115 Rp = 2.72; Rwp = 3.46; Rexp = 3.33; x2 = 1.08.

x

y

z

Bond length

Bond angle

0.5202(6) 0.0 0.5 0.395(3) 0.202(9) 0.190(7)

0.5692(3) 0.5 0.0 0.957(3) 0.195(8) 0.081(5)

0.253(1) 0.0 0.0 0.265(6) 0.020(7) 0.081(5)

Ni-O1(x2) = 1.84 Ni-O2(x2) = 2.08 Ni-O3(x2) = 2.02 Mn-O1 (x2) = 2.09 Mn-O2 (x2) = 1.84 Mn-O1 (x2) = 2.05

= 144.64 = 152.25 = 138.70

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no significant change is observed in the UV–vis absorption spectrum of the DNMO-2 sample. 3.3. Dielectric relaxation The dielectric relaxation of DNMO can be broadly analyzed in terms of (i) dipolar and (ii) conductivity relaxation mechanisms. For dielectric relaxation originating from dipole motion, the dielectric response can be described as a direct relationship between the dielectric constant (e* = e0  ie00 ) and the admittance. For conductivity relaxation, the dispersion of the dielectric constant is determined by a locally inhomogeneous potential barrier with long-range charge-carrier diffusion, and the dielectric response can be described as a relationship between electric modulus (M* = M0 + iM00 = 1/e*) and the impedance (Z* = Z0 + iZ00 ). We have applied the second approach to study the dielectric relaxation of DNMO. The angular frequency dependence of real (Z0 ) and imaginary (Z00 ) parts of complex impedance of DNMO-1 at various temperatures are shown in Fig. 5. At a particular temperature, Z0 decreases monotonically with increasing frequency upto a certain frequency and then becomes frequency independent (Fig. 5(a)). It is evident from Fig. 5(b) that the spectrum of Z00 at each temperature exhibits one relaxation peak whose peak frequency, vm, increases with increasing temperature. It should be noted that the similar spectrum are also observed in the sample DNMO-2 (not shown). This behaviour suggests a possibility that the spectral intensity of the dielectric relaxation observed in DNMO is thermally activated. The total resistance decreases with an increase in temperature across the entire frequency range, which shows the semiconducting behaviour of the material. It is clear that the width of the peaks in Fig. 5(b) cannot be accounted for in terms of a mono-dispersive relaxation process, but points towards the possibility of a distribution of relaxation times. In order to account for it, fitting of the impedance data was performed with the help of the Cole–Cole relation, defined as [25] Fig. 3. SEM images of surface morphologies of (a) DNMO-1 and (b) DNMO-2.

253 K 289 K 1 325 K 352 K 370 K 388 K 415 K Fitting Z' (MΩ)

16 12 Z' (MΩ)

2 for the direct or indirect transition respectively. Using this relation, a graph is plotted between (ahy)2 and hy as shown in Fig. 4. The extrapolation of the linear absorption-edge part of this graph with a straight line to (ahy)2 = 0 axis gives the value of the band gap. The value of the optical band gap of the material for direct transition is found to be
1.62 eV. It is to be mentioned that

8

0

3

4

4

5 -1

log ω (rad s )

(a)

0 4

2

-2

Z'' (MΩ)

Z'' (MΩ)

2

(αhν) (m eV )

12

8

0

2

3

4

E g = 1.62 eV

0.5

4 5 6 -1 log ω (rad s )

(b)

0 0 0.5

1.0

1.5

2.0

2.5

3.0

h ν (eV) Fig. 4. UV–vis absorption spectrum for direct transition ((ahy)2 vs. hy).

7

3

4 5 -1 log ω (rad s )

6

Fig. 5. Frequency (angular) dependence of Z0 (a) and Z00 (b) of DNMO at various temperatures. The solid lines are fits of the Cole–Cole relation.

S. Chanda et al. / Materials Research Bulletin 62 (2015) 153–160

Z ¼

Rg  1a 1 þ jvt g

(2)

where Rg and t g are the resistance and characteristic relaxation time respectively corresponding to grain effect, and a is a dimensionless exponent that denotes the angle of tilt of the circular arc from the real axis. The best fitting of the impedance data with Eq. (2) is shown by solid lines in Fig. 5 for Z0 and Z00 . The values of a lie in the range between 0.23 and 0.18 in the temperature range of 253–415 K. To get an idea about the type of relaxation response in these materials, it is necessary to find out the activation energy of relaxation process. At a temperature T, the most probable relaxation frequency (vm) corresponding to the peak position in Z00 vs. log v is proportional to exp(Ea/kBT) (Arrhenius law). The linear fit of the experimental data as shown by the solid lines in Fig. 6 gives the activation energy of 0.364 and 0.344 eV for DNMO-1 and DNMO-2, respectively. Such a value of activation energy indicates that the conduction mechanism in the samples may be due to the polaron hopping based on the electron carriers [26]. The fact that the lower activation energy in DNMO-2 than that of DNMO-1 is due to the increase in density (decrease in porosity) of the sample with increase in sintering temperature which gives a better contact between the particles and provides an easy percolation path for the charge carrier conduction [27]. In Fig. 7, the variation of normalized parameters M00 /M00 m and Z00 / Z00 m as a function of logarithmic frequency measured at 415 K for DNMO-1 is shown. The position of the peak in the Z00 /Z00 m is slightly shifted to lower frequency region in relation to the M00 /M00 m peak. This is also observed in DNMO-2 (not shown). A comparison of the impedance with electric modulus data allows the determination of the grain response in terms of localized or non-localized conduction [28]. The Debye model is related to an ideal frequency response of localized relaxation. The non-localized process known as the dc conductivity is dominated at low frequencies. The overlapping peak position of M00 /M00 m and Z00 /Z00 m curves is an evidence of delocalized or long-range relaxation [28]. For DNMO the M00 /M00 m and Z00 /Z00 m peaks almost overlap suggesting the major components from long-range relaxations.The inset of Fig. 7 shows complex plane impedance plot, (Z* plot), for the DNMO-1, plotting the imaginary part Z00 against the real part Z0 at temperature 415 K. A point on this curve represents a given measurement of Z0 (v) and Z00 (v), at a specific angular frequency v (=2pf). In the complex impedance plot, one expects a separation of the grain effect from

6.0

Fig. 7. Frequency (angular) dependence of normalized peaks, Z00 /Z00 m and M00 /M00 m for DNMO-1 at 415 K. The scaling behaviour of the Z00 of DNMO-1 is shown in the

surface (grain boundary and/or electrode) effect as the surface polarization is highly capacitive phenomenon and is characterized by large relaxation time than the polarization mechanism in the grain. This fact usually results in the appearance of two separate arcs of semicircle in the Z00 vs. Z0 plots (one representing the bulk effect at high frequencies while the other represents surface effect in lower frequency range). The presence of a single semicircular arc passing through the origin in the entire frequency region indicates that the relaxation mechanism in DNMO is purely a grain effect. If we scale each Z00 with Z00 m and each v with vm, the entire curves collapse into a single master curve as shown in the inset of Fig. 7. The scaling nature of Z00 implies that the relaxation shows the same mechanism in the entire temperature range. 3.4. dc and ac conductivity To study the long range relaxation phenomena in DNMO, we have also adopted the dc and ac conductivity formalisms. Fig. 8 shows I–V characteristics obtained at different temperatures for DNMO-1. The dc conduction study also supports the insulating behaviour of the material. It should be noted that the similar characteristics are also observed in the sample DNMO-2 (not shown). The corresponding Arrhenius plot is shown in the inset of Fig. 8. The temperature dependence of dc conductivity of DNMO1 for polaron hopping can be explained by [25]   W H þ eg =2 n a2 e2 vLO exp  s dc ¼ 0 kB T kB T

4.5 DNMO2

¼

Ea = 0.36 eV

-1

log ωm (rad s )

5.5

4.0 5.0 DNMO1

3.5

Ea = 0.34 eV

4.5

3.0 4.0

2.4

157

2.6

2.8

3.0

3.2

3.4

-1

1000/T (K ) Fig. 6. The temperature dependence of the most probable relaxation frequency obtained from the frequency-dependent imaginary part of the impedance curves for DNMO-1 and DNMO-2: here, the symbols are the experimental data and the solid lines are the least-squares straight-line fit. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

  W H þ eg =2 A0 exp  kB T T

(3)

where e denotes the electronic charge, n0 expðeg =2kB TÞ is the number of small polaron per unit volume, a is the characteristic intersite hopping distance, vLO is the optical phonon frequency, WH is the hopping energy of a polaron, and eg is the energy gap between the energy states which participate directly in the electrical transport. The dc activation energy ðW H þ eg =2Þ as obtained from the linear fit of the experimental data (shown in the inset of Fig. 8) is found to be 0.37 eV which is very close to activation energy required for relaxation process as obtained from the impedance analysis. These results imply that the nature of charge carriers responsible for dielectric relaxation peaks and dc conduction belongs to the same category, indicating that the polarization relaxation has a close relation to the conductivity in

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s ðvÞ ¼ s dc 1 þ

-1

σdcT (Sm K)

0

0.08

-2

I (mA)

-4 2 248 K 288 K 318 K 333 K 353 K

0.04

3 4 -1 1000/T (K )

0.0 0

10

20

30

40

50

V (volt) Fig. 8. Current vs voltage characteristics at different temperature for DNMO-1. Temperature dependence of dc conductivity of DNMO-1 is shown in the inset.

the grain interior. In such situation the band gap energy for electrical conduction eg can be calculated from the difference between the dc activation energy and hopping energy of small polaron. In the case of dielectric relaxation, the activation energy is the hopping energy [25], i.e., Ea = WH. Thus the value of eg is found to be 0.058 eV. The least-mean-square analysis also yields Ao = 5.06  106 K V1 cm1. Fig. 9 shows a log–log plot of the frequency dependence of ac conductivity for DNMO at various temperatures. The value of ac conductivity decreases with decreasing frequency and becomes independent of frequency after a certain value. Extrapolation of this part to lower frequencies will give the dc conductivity (s dc). It is to be mentioned that, at low frequencies, random diffusion of charge carriers via hopping gives rise to a frequency-independent conductivity. At high frequencies, s (v) exhibits dispersion, increasing in a power-law fashion. The real part of conductivity s in such a situation can be expressed as [29]

-1

log σac (Sm )

(a) -4 253 K 289 K 325 K 352 K 370 K 388 K 415 K Fitting

-5

-1

log σac (Sm )

(b) -3.5



v vH

n  (4)

where vH is the hopping frequency of the charge carriers, and n is the dimensionless frequency exponent. This relation corresponds to the hopping conduction of charge carriers. Hopping of charge carriers takes place through localization positions separated by energy barriers of various heights. The number of charge carriers that have high relaxation time due to high energy barrier which respond in the low-frequency regime might be lower than the number of charge carriers with low relaxation time, and this has resulted in low values of conductivity at low frequencies. The temperature-dependent parameter n represents the number of many-body interactions among charge carriers and defect states. In a fixed frequency range, n ! 1 as T ! 0 and decreases with increasing temperature, indicating fewer interactions. The experimental conductivity spectra of DNMO is fitted to Eq. (4) with s dc and vH as variables, keeping in mind that the values of the parameter n are weakly temperature dependent. The best fit of the conductivity spectra is shown by solid lines in Fig. 9(a) with the values of n lying in the range between 0.88 and 0.95 for the temperature range from 253 to 415 K. A comparison of the frequency dependent ac conductivity for DNMO-1 and DNMO2 at the temperature 370 and 415 K has been shown in the Fig. 9(b). It is observed that the electrical conductivity increases with increasing sintering temperature which can be ascribed to the decrease in porosity as shown in Fig. 3. With increasing sintering temperature, the relative density of the materials increases, ensuring a better contact between the particles, which is demonstrated through higher relative conductivities. 3.5. Electronic and magnetic structure The spin polarized total density of states (DOS) per formula unit of DNMO obtained by only GGA calculations is shown in Fig. 10. The zero of the energy is set at the top of the valence band. Without accounting for Coulomb repulsion i.e., U = 0, the GGA calculations predict that the ground state of DNMO has half-metallic character with a finite density of states at the Fermi level (set at 0 eV) in the down spin channel and a band gap of size 1.4 eV in the up spin channel. This half-metallic behaviour does not agree with our experimental results which show that DNMO is an insulator with a direct energy band gap of 1.62 eV. It is well known that LDA and GGA cannot describe the correct ground state for perovskite oxides and other highly correlated compounds [30,31]. Hence, special considerations are required for the correlation effect of d and f electrons of Ni, Mn, and Dy in DNMO. We have therefore

370_DNMO-2 415_DNMO-2 370_DNMO-1 415_DNMO-1

-4.0

-4.5 4 -1 log ω (rad s )

6

Fig. 9. (a) Frequency (angular) dependence of ac conductivity of DNMO-1 at various temperatures. Solid lines are fits of the power law. (b) Frequency (angular) dependence of ac conductivity of DNMO-1 and DNMO-2 for the temperatures 370 and 415 K.

Fig. 10. The spin-polarized total density of states calculated within GGA for DNMO.

S. Chanda et al. / Materials Research Bulletin 62 (2015) 153–160

50

DNMO. The sum of the magnetic moments of Ni and Mn in DNMO is found to be 4.43 mB/f.u. Since the magnetic interaction between the magnetic cations Ni and Mn takes place through the O anion, Osite possesses some magnetic moment of 0.18 mB/f.u. The rest of the moment comes from Dy3+ ions in DNMO as the total magnetic moment are found to be 15.0 mB/f.u. This is in a good agreement with the experimental results obtained in DyNi0.5Mn0.5O3 by Asai et. al [7].

DNMO

0 50 12 Dy-f

DOS (States/eV cell)

0 12 2

4. Conclusions

eg

t2g

Ni-d

0 t2g

3

eg

t2g

1.5 Mn-d

eg

0.00 4 0.7

159

t2g

eg

2

4

O-p

0.0 0.7 -10

-8

-6

-4

-2

0

6

Energy (eV) Fig. 11. The spin-polarized total and partial density of states calculated within GGA + U for DNMO.

considered the GGA + U approach, where a Hubbard term (U) is introduced for the strong on-site Coulomb repulsion among the various states [30].The spin polarized total DOS with partial DOS of Dy-f, Ni-d, Mn-d and O-p states of DNMO obtained from GGA + U calculations is shown in Fig. 11. The GGA + U calculations predict correctly the insulating electronic structure of DNMO. The optical band gap is found to be
1.5 eV which is almost equal to the experimental value observed by UV–vis absorption spectrum of DNMO. It is observed from the partial DOS of Ni-d and Mn-d that the octahedral crystal field in the surroundings of Ni and Mn atoms splits the Ni- and Mn-d manifolds into t2g and eg levels. In the upspin channel, the Ni-t2g and Ni-eg levels are found in the energy range from 6 eV to EF with the significant mixing with Mn-d states and O-2p states. In the down spin channel, Ni-t2g states lie from 1.2 to 0.5 eV in the valence band, while Ni-eg states lie from 1.5 to 3.0 eV in the conduction band. This leads to the

8 2" 3# conclusion that the nominal oxidation state of Ni is d : t3" 2g eg t 2g in DNMO. In the up-spin channel the Mn-t2g states are localized between Ni-t2g and Ni-eg states and filled, while the Mn-eg states lie from 1.5 to 2.8 eV and remain empty. In the down-spin channel, both Mn-t2g and Mn-eg states are located in the energy range from 1.5 to 5.0 eV. This corresponds to the nominal valence of Mn4+

3 0 in DNMO, which shows a good agreement of the d : t3" 2g eg results reported by Asai et. al [7]. Exchange splitting between t2g up and t2g down, and between eg up and eg down are also observed for both Ni and Mn ions. The exchange splitting between eg up and eg down states for Ni and Mn is 1.2 and 1.0 eV respectively, and the exchange splitting between t2g up and t2g down states for Ni and Mn is 0.5 and 2.5 eV respectively. The calculated magnetic moments at Ni and Mn-sites are found to be 1.56 and 2.87 mB/f. u., respectively which also support the Ni2+ and Mn4+ states in

In summary, we have synthesised double perovskite Dy2NiMnO6 in nano and bulk phases by the sol–gel citrate method and systematically investigated its structural, dielectric, and magnetic properties. The Rietveld refinement of X-ray diffraction pattern of the sample at room temperature (300 K) shows the monoclinic P21/n phase. The value of the optical band gap of the material for direct transition is found to be
1.62 eV. The dielectric relaxation (a conduction process) of the sample is investigated in the impedance and electric modulus formalisms in the frequency range from 50 Hz to 1 MHz and in the temperature range from 253 to 415 K. The Cole–Cole model is used to explain the relaxation mechanism in DNMO. The frequency-dependent maxima in the imaginary part of impedance are found to obey an Arrhenius law with activation energy of 0.346 and 0.344 eV for nano and bulk DNMO respectively. The dc and ac conductivity formalisms reveal that small polaron hopping process is responsible for conduction in DNMO. With increasing sintering temperature, the relative density of the materials increases and porosity decreases, ensuring a better contact between the particles, which is demonstrated through higher relative conductivities. The GGA + U calculated results obtained from FPLAPW method suggest that the ground state of the material is a ferromagnetic insulator. Acknowledgements Sujoy Saha acknowledges the financial support provided by the UGC, New Delhi (India) in the form of SRF. Alo Dutta thanks to Department of Science and Technology for providing the financial support through DST Fast Track Project under grant no. SR/FTP/ PS-032/2010. References [1] N.S. Rogado, J. Li, A.W. Sleight, M.A. Subhraminian, Adv. Mater. 17 (2005) 2225. [2] D. Choudhury, P. Mandal, R. Mathieu, A. Hazarika, S. Rajan, A. Sundaresan, U.V. Waghmare, R. Knut, O. Karis, P. Nordblad, D.D. Sarma, PRL 108 (2012) 127201. [3] M. Sonobe, K. Asai, J. Phys. Soc. Jpn. 61 (1992) 4193. [4] C. Shi, Y. Hao, Z. Hu, J. Phys. D: Appl. Phys. 44 (2011) 245405. [5] S. Zhao, L. Shi, S. Zhou, J. Zhao, H. Yang, Y. Guo, J. Appl. Phys. 106 (2009) 123901. [6] K. Devi Chandrasekhar, A.K. Das, C. Mitra, A. Venimadhav, J. Phys.: Condens. Matter 24 (2012) 495901. [7] K. Asai, K. Fujiyoshi, N. Nishimori, Y. Satoh, Y. Kobayashi, M. Mizoguchi, J. Phys. Soc. Jpn. 67 (1998) 4218. [8] K.D. Truong, M.P. Singh, S. Jandl, P. Fournier, J. Phys.: Condens. Matter 23 (2011) 052202. [9] W.Z. Yang, X.Q. Liu, H.J. Zhao, Y.Q. Lin, X.M. Chen, J. Appl. Phys. 112 (2012) 064104. [10] C. Moure, J. Tart aj, A. Moure, O. Peña, Bol. Soc. Esp. Ceram. 48 (2009) 199. [11] H.S. Nair, D. Swain, N. Hariharan, S. Adiga, C. Narayana, S. Elzabeth, J. Appl. Phys. 110 (2011) 123919. [12] M. Mouallem-Bahout, T. Roisnel, G. Andre, D. Gutierrez, C. Moure, O. Peña, Solid State Commun. 129 (2004) 255. [13] R.J. Booth, R. Fillman, H. Whitaker, A. Nag, R.M. Tiwari, K.V. Ramanujachary, J. Gopalakrishnan, S.E. Lofland, Mater. Res. Bull. 44 (2009) 1559. [14] P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, J. Luitz, WIEN2k, An Augmented PlaneWave + Local Orbitals Program for Calculating Crystal Properties (Techn. Universität Wien Vienna, 2001) [15] S. Chanda, S. Saha, A. Dutta, T.P. Sinha, Mater. Res. Bull. 48 (2013) 1688. [16] S. Saha, S. Chanda, A. Dutta, T.P. Sinha, J. Sol–Gel Sci. Technol. 69 (2014) 553. [17] J. Rodriguez-Carvajal, Physica B 192 (1993) 55. [18] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865.

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